Increases in the sensitivity of DNA profiling technology now allow profiles to be obtained from smaller and more degraded DNA samples than was previously possible. The resulting profiles can be highly informative, but the subjective elements in the interpretation make it problematic to achieve the valid and efficient evaluation of evidential strength required in criminal cases. The problems arise from stochastic phenomena such as "dropout" (absence of an allele in the profile that is present in the underlying DNA) and experimental artefacts such as "stutter" that can generate peaks of ambiguous allelic status. Currently in the UK, evidential strength evaluation uses an approach in which the complex signals in the DNA profiles are interpreted in a semi-manual fashion by trained experts aided by a set of guidelines, but also relying substantially on professional judgment. We introduce a statistical model to calculate likelihood ratios for evaluating DNA evidence arising from multiple known and unknown contributors that allows for such stochastic phenomena by incorporating peak heights. Efficient use of peak heights allows for more crime scene profiles to be reported to courts than is currently possible. The model parameters are estimated from experimental data incorporating multiple sources of variability in the profiling system. We report and analyse experimental results from the SGMPlus system, run at 28 amplification cycles with no enhancements, currently used in the UK. Our methods are readily adapted to other DNA profiling systems provided that the experimental data for the parameter estimation is available.